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1

Dunkel, Jörn. "Relativistic Brownian motion and diffusion processes." kostenfrei, 2008. http://d-nb.info/991318757/34.

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Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.

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The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-P

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3

Keprta, S. "Integral tests for Brownian motion and some related processes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ26856.pdf.

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Keprta, Stanislav Carleton University Dissertation Mathematics and Statistics. "Integral tests for Brownian motion and some related processes." Ottawa, 1997.

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5

Cakir, Rasit Grigolini Paolo. "Fractional Brownian motion and dynamic approach to complexity." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3992.

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6

Simon, Matthieu. "Markov-modulated processes: Brownian motions, option pricing and epidemics." Doctoral thesis, Universite Libre de Bruxelles, 2017. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/250010.

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This thesis is devoted to the study of different stochastic processes which have a common feature: they are Markov-modulated, which means that their evolution rules depend on the state occupied by an underlying Markov process. In the first part of this thesis, we analyse the stationary distribution and various first passage problems for Markov-modulated Brownian motions (MMBMs) as well as for two extensions: MMBMs with jumps and MMBMs modified by a temporary change of regime upon visits to level zero. The second part of this thesis is devoted to the use of Markov-modulated processes in mathema

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7

莊競誠 and King-sing Chong. "Explorations in Markov processes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235682.

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Chong, King-sing. "Explorations in Markov processes /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18736105.

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9

Duncan, Thomas. "Brownian Motion: A Study of Its Theory and Applications." Thesis, Boston College, 2007. http://hdl.handle.net/2345/505.

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Thesis advisor: Nancy Rallis<br>The theory of Brownian motion is an integral part of statistics and probability, and it also has some of the most diverse applications found in any topic in mathematics. With extensions into fields as vast and different as economics, physics, and management science, Brownian motion has become one of the most studied mathematical phenomena of the late twentieth and early twenty-first centuries. Today, Brownian motion is mostly understood as a type of mathematical process called a stochastic process. The word "stochastic" actually stems from the Greek word for "I

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10

Hult, Henrik. "Topics on fractional Brownian motion and regular variation for stochastic processes." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3604.

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<p>The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof fu

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11

Hartung, Lisa Bärbel [Verfasser]. "Extremal Processes in Branching Brownian Motion and Friends / Lisa Bärbel Hartung." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1113688432/34.

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12

Overbeck, Ludger. "Konditionierungen der Super-Brownsche-Bewegung und verzweigender Diffusionen." Bonn : [s.n.], 1992. http://catalog.hathitrust.org/api/volumes/oclc/29044483.html.

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13

Cakir, Rasit. "Fractional Brownian motion and dynamic approach to complexity." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3992/.

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The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is well known that the recrossing times of the origin by an ordinary 1D diffusion trajectory generates a distribution of time distances between two consecutive origin recrossing times with an inverse power law with index m=1.5. However, with theoretical and numerical arguments, it is proved that this is th

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14

Erdogan, Ahmet Yasin. "Analysis of the effects of phase noise and frequency offest in orthogonal frequency division multiplexing (OFDM) systems /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Mar%5FErdogan.pdf.

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Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2004.<br>Thesis advisor(s): Murali Tummala, Roberto Cristi. Includes bibliographical references (p. 127-129). Also available online.

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15

Lappala, Anna. "Molecular dynamics simulations : from Brownian ratchets to polymers." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709251.

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16

Sanyal, Suman. "Stochastic dynamic equations." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Sanyal_09007dcc80519030.pdf.

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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.<br>Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references (p. 124-131).

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17

Maher, David Graham School of Mathematics UNSW. "Brownian motion and heat kernels on compact lie groups and symmetric spaces." Awarded by:University of New South Wales. School of Mathematics, 2006. http://handle.unsw.edu.au/1959.4/28295.

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An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and ildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It??o type stochastic differential equations and applying the Feynman-Ka??c theorem. We also consider wr

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18

Wu, Tung-Lung Jr. "Linear and non-linear boundary crossing probabilities for Brownian motion and related processes." Applied Probability Trust - Journal of Applied Probability, 2010. http://hdl.handle.net/1993/8123.

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We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our met

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19

Tanner, Stephen. "Non-tangential and conditioned Brownian convergence of pluriharmonic functions /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5729.

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20

Bessada, Dennis Fernandes Alves. "Generalizações do movimento browniano e suas aplicações à física e a finanças /." São Paulo : [s.n.], 2005. http://hdl.handle.net/11449/91854.

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Orientador: Gerson Francisco<br>Banca: Victo dos Santos Filho<br>Banca: Fernando Manoel Ramos<br>Resumo: Realizamos neste trabalho uma exposição geral da Teoria do Movimento Browniano, desde suas primeiras observações, feitas no âmbito da Biologia, até sua completa descrição seundo as leis da Mecânica estatística, formulação esta efetuada por Einstein em 1905. Com base nestes princípios físicos analisamos a Teoria do Movimento Browniano de Einstein como sendo um processo estocástico, o que permite sua generalização para um processo de Lévy. Fazemos uma exposição da Teoria de Lévy, e aplicamo-l

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21

Nouri, Suhila Lynn. "Expected maximum drawdowns under constant and stochastic volatility." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050406-151319/.

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22

Swanson, Jason. "Variations of stochastic processes : alternative approaches /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5733.

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Bessada, Dennis Fernandes Alves [UNESP]. "Generalizações do movimento browniano e suas aplicações à física e a finanças." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/91854.

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Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-04Bitstream added on 2014-06-13T20:48:05Z : No. of bitstreams: 1 bessada_dfa_me_ift.pdf: 3052096 bytes, checksum: bfe2b25d2283cf5ec06ca7dc7407c70c (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Realizamos neste trabalho uma exposição geral da Teoria do Movimento Browniano, desde suas primeiras observações, feitas no âmbito da Biologia, até sua completa descrição seundo as leis da Mecânica estatística, formulação esta efetuada por Einstein em 1905. Com base nestes

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24

Corry, Ben Alexander. "Simulation studies of biological ion channels." View thesis entry in Australian Digital Theses Program, 2002. http://thesis.anu.edu.au/public/adt-ANU20030423.162927/index.html.

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25

Lyons, Simon. "Inference and parameter estimation for diffusion processes." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10518.

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Diffusion processes provide a natural way of modelling a variety of physical and economic phenomena. It is often the case that one is unable to observe a diffusion process directly, and must instead rely on noisy observations that are discretely spaced in time. Given these discrete, noisy observations, one is faced with the task of inferring properties of the underlying diffusion process. For example, one might be interested in inferring the current state of the process given observations up to the present time (this is known as the filtering problem). Alternatively, one might wish to infer pa

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26

Vardar, Ceren. "On the Correlation of Maximum Loss and Maximum Gain of Stock Price Processes." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1224274306.

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27

Ufuktepe, Ünal. "Positive solutions of nonlinear elliptic equations in the Euclidean plane /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9841364.

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28

Osborn, Allan Ray. "Flow control methods in a high-speed virtual channel." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/13521.

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29

Zhou, Wei, and 周硙. "Topics in optimal stopping with applications in mathematical finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46582046.

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30

Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.

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Thesis (MSc)--Stellenbosch University, 2015<br>ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian

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31

Al-Talibi, Haidar. "On the Relevance of Fractional Gaussian Processes for Analysing Financial Markets." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1762.

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<p>In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept o

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32

Long, Brian Russell. "Transport of polymers and particles in microfabricated array devices /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2008. http://hdl.handle.net/1794/8289.

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Thesis (Ph. D.)--University of Oregon, 2008.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 122-127). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

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33

Delorme, Mathieu. "Processus stochastiques et systèmes désordonnés : autour du mouvement Brownien." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE058/document.

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Dans cette thèse, on étudie des processus stochastiques issus de la physique statistique. Le mouvement Brownien fractionnaire, objet central des premiers chapitres, généralise le mouvement Brownien aux cas où la mémoire est importante pour la dynamique. Ces effets de mémoire apparaissent par exemple dans les systèmes complexes et la diffusion anormale. L’absence de la propriété de Markov rend difficile l’étude probabiliste du processus. On développe une approche perturbative autour du mouvement Brownien pour obtenir de nouveaux résultats, sur des observables liées aux statistiques des extrêmes

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34

Baumgarten, Christoph [Verfasser], and Frank [Akademischer Betreuer] Aurzada. "Persistence of sums of independent random variables, iterated processes and fractional Brownian motion / Christoph Baumgarten. Betreuer: Frank Aurzada." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1035276445/34.

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35

Herdiana, Ratna. "Numerical methods for SDEs - with variable stepsize implementation /." [St. Lucia, Qld.], 2003. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17638.pdf.

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36

Benjamin, Ronald. "Stochastic energetics of the Büttiker-Landauer motor and refrigerator." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2008p/benjamin.pdf.

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Thesis (Ph. D.)--University of Alabama at Birmingham, 2008.<br>Additional advisors: Renato Camata, Nikolai Chernov, Perry A. Gerkines, Gunter Stolz. Description based on contents viewed Feb. 9, 2009; title from PDF t.p. Includes bibliographical references (p. 123-129).

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37

Arikan, Ali Ferda. "Structural models for the pricing of corporate securities and financial synergies : applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.

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Mergers are the combining of two or more firms to create synergies. These synergies may come from various sources such as operational synergies come from economies of scale or financial synergies come from increased value of securities of the firm. There are vast amount of studies analysing operational synergies of mergers. This study analyses the financial ones. This way the dynamics of purely financial synergies can be revealed. Purely financial synergies can be transformed into financial instruments such as securitization. While analysing financial synergies the puzzle of distribution of fi

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38

Arikan, Ali F. "Structural models for the pricing of corporate securities and financial synergies. Applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.

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Mergers are the combining of two or more firms to create synergies. These synergies may come from various sources such as operational synergies come from economies of scale or financial synergies come from increased value of securities of the firm. There are vast amount of studies analysing operational synergies of mergers. This study analyses the financial ones. This way the dynamics of purely financial synergies can be revealed. Purely financial synergies can be transformed into financial instruments such as securitization. While analysing financial synergies the puzzle of distributio

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39

Suzuki, Kohei. "Convergence of stochastic processes on varying metric spaces." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215281.

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40

Gomez-Solano, Juan Rubén. "Nonequilibrium fluctuations of a Brownian particle." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00680302.

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This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is

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41

Serrano, Francisco de Castilho Monteiro Gil. "Fractional processes: an application to finance." Master's thesis, Instituto Superior de Economia e Gestão, 2016. http://hdl.handle.net/10400.5/13002.

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Mestrado em Matemática Financeira<br>Neste trabalho é apresentada uma extensa descrição matemática, orientada para a modelação financeira, de três principais processos fracionários: o processo Browniano fracionário e os dois processos de Lévy fracionários. Mostram-se como estes processos podem ser originados. É explorado o conceito de auto-semelhança e apresentamos algumas noções de cálculo fracionário. Também é discutido o lugar destes processos no problema de encontrar o preço de derivados financeiros e apresentamos uma nova abordagem para a simulação do processo de Lévy fracionário que perm

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42

Lee, Joongsup. "New control charts for monitoring univariate autocorrelated processes and high-dimensional profiles." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42711.

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In this thesis, we first investigate the use of automated variance estimators in distribution-free statistical process control (SPC) charts for univariate autocorrelated processes. We introduce two variance estimators---the standardized time series overlapping area estimator and the so-called quick-and-dirty autoregressive estimator---that can be obtained from a training data set and used effectively with distribution-free SPC charts when those charts are applied to processes exhibiting nonnormal responses or correlation between successive responses. In particular, we incorporate the two estim

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43

Popovic, Ray. "Parameter estimation error: a cautionary tale in computational finance." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34731.

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We quantify the effects on contingent claim valuation of using an estimator for the volatility of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After substituting into the GBM the direct volatility estimator for the true, but unknown, value of the parameter sigma, we derive the resulting marginal distribution of the approximated GBM. This allows us to derive post

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44

Antonini, Claudia. "Folded Variance Estimators for Stationary Time Series." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6931.

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This thesis is concerned with simulation output analysis. In particular, we are inter- ested in estimating the variance parameter of a steady-state output process. The estimation of the variance parameter has immediate applications in problems involving (i) the precision of the sample mean as a point estimator for the steady-state mean and #956;X, and (ii) confidence intervals for and #956;X. The thesis focuses on new variance estimators arising from Schrubens method of standardized time series (STS). The main idea behind STS is to let such series converge to Brownian bridge processes; then

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45

Misiran, Masnita. "Modeling and pricing financial assets under long memory processes." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/2549.

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An important research area in financial mathematics is the study of long memory phenomenon in financial data. Long memory had been known long before suitable stochastic models were developed. Fractional Brownian motion (FBM) can be used to characterize this phenomenon. This thesis examines the use of FBM and its long memory parameter H, from the view point of estimation method, approximation, and numerical performance.How to estimate the long memory parameter H is important in financial pricing. This thesis starts by reviewing the performance of some existing preliminary methods for estimating

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46

Schmid, Patrick. "Random processes in truncated and ordinary Weyl chambers." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-66394.

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The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximat

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47

Duhalde, Jean-Pierre. "Sur des propriétés fractales et trajectorielles de processus de branchement continus." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066029/document.

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Cette thèse étudie certaines propriétés fractales et trajectorielles de processus de branchement en temps et espace continus. De façon informelle, ce type de processus est obtenu en considérant l'évolution d'une population où les individus se reproduisent et meurent au cours du temps, et ce de manière aléatoire. Le premier chapitre concerne la classe des processus de branchement avec immigration. On donne une formule semi-explicite pour la transformée de Laplace des temps d'atteinte ainsi qu'une condition nécessaire et suffisante de récurrence-transience. Ces deux résultats illustrent la compé

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48

Afonso, Maria de Lourdes Belchior. "Evaluation of ruin probabilities for surplus processes with credibility and surplus dependent premiums." Doctoral thesis, Instituto Superior de Economia e Gestão, 2008. http://hdl.handle.net/10400.5/1113.

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Doutoramento em Matemática Aplicada à Economia e Gestão<br>In this dissertation we present a method for the numerical evaluation of the ruin prob¬ability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simu¬lation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin

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Pereira, Gonçalo André Nunes. "Modelling sovereign debt with Lévy Processes." Master's thesis, Instituto Superior de Economia e Gestão, 2014. http://hdl.handle.net/10400.5/7611.

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Mestrado em Ciências Actuariais<br>Propomos modelizar o risco de crédito soberano de cinco países da zona Euro (Portugal, Irlanda, Itália, Grécia e Espanha) seguindo uma abordagem estrutural de primeira passagem em que o movimento Browniano geométrico é substituído por um processo de Lévy regido apenas por uma componente de saltos. Deste modo, introduzimos incrementos assimétricos e leptocúrticos e a possibilidade de incumprimento instantâneo, removendo assim algumas das principais limitações do modelo Black-Scholes. Calculamos a probabilidade de sobrevivência como preço de uma opção barreira

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Triampo, Wannapong. "Non-Equilibrium Disordering Processes In binary Systems Due to an Active Agent." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/26738.

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In this thesis, we study the kinetic disordering of systems interacting with an agent or a walker. Our studies divide naturally into two classes: for the first, the dynamics of the walker conserves the total magnetization of the system, for the second, it does not. These distinct dynamics are investigated in part I and II respectively. In part I, we investigate the disordering of an initially phase-segregated binary alloy due to a highly mobile vacancy which exchanges with the alloy atoms. This dynamics clearly conserves the total magnetization. We distinguish three versions of dynamic rules

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